As was to be expected, Corbyn came out firing on all cylinders in his speech to the party faithful in Brighton. Labour, he said, "was now the political mainstream," and "ready for government." Addressing Brexit, he accused Prime Minister Theresa May of "self-interested bungling" and said that Labour was "ready to build a new and progressive relationship with Europe."

While Corbyn basks in his party's new-found glory, Germany's Social Democrats (SPD) can only dream of such good fortune.

Read more: German and British political parties: A comparison

Depressingly for them, it's not that long ago when they went from a spent force, staring into an electoral abyss, to a party reaching giddy heights in the polls — by their standards — transformed by Martin Schulz who briefly breathed some life into the party.

It couldn't and didn't last. In Sunday's election the SPD barely scraped 20 percent of the vote and has decided that its best chance at recuperation now lies on the opposition benches in the German parliament.

Across the Channel, the UK's Labour party knows that feeling all too well. From its heyday under then party leader and Prime Minister Tony Blair who ushered in a new and cool Britannia — which interestingly went hand in hand with the SPD's centrist glory days under former Chancellor Gerhard Schröder — the party then spent years in the wilderness beset by infighting and a dramatic loss of support from its traditional voter base.

But in the wake of the UK's Brexit referendum and Prime Minister May's ill-judged decision to hold early elections in June in a bid to shore up support for her Conservative Party, Labour has woken from its slumber.

Labour awakens

Credit for its revival has to go to Corbyn, who has managed to take advantage of May's confusing and confused Brexit policy by positioning Labour as a clear counterpart to the Tory government. "Corbyn has managed to offer a real alternative to the current British government and the political mainstream — which is something for example the SPD has not managed to do," says Leopold Traugott, a policy analyst at Open Europe, an independent think tank focusing on the UK's relationship with the EU.

According to Charlie Lees, a politics professor at Bath University who specializes in comparative party systems, Corbyn has surprised himself. "He was allowed on the ballot because it's been a tradition in the Labour Party that its center-right [faction] allows a left wing candidate to run and, as in the past, they expected Corbyn to be thoroughly beaten."

Read more: UK establishment fighting 'proxy war' against Corbyn

Crucially, says Lees, the UK economy has lapped up globalization more than any other major industrial country over the last 25 years. "The backlash against this kind of technocratic, pro-globalization agenda has been felt by parties on both sides, but particularly by Social Democratic parties since the late 90s." That frustration, he says, has reared its head quicker inside the Labour Party than inside the SPD, thus thrusting Corbyn into the limelight.

Notwithstanding Labour's pro-Brexit position, the desire for change within parts of British society appears to be a key driving force in Labour's change in fortunes. That and Corbyn's authenticity, says Lees.  "[Corbyn's] offer is essentially a retro 1970 offer but nevertheless for a new generation of activists in particular it seemed fresh."

Smoke and mirrors on Brexit

And Corbyn's opaque position on Brexit has, so far at least, done little to damage his standing. "Labour is incredibly divided and constantly flip-flopping on Brexit. There is no clear position on Brexit, but that makes it better to defend because there is no clear stance," says Traugott.

Lees concurs that "they're desperate to keep this sort of smoke and mirrors over Brexit going and as the opposition they're able to do because they don't have to commit. I was very frustrated seeing people who are essentially very strongly pro-EU projecting their wishes onto Corbyn saying 'he's a pro-European because he's a good guy,' without realizing that there is actually a very strong tradition of left-wing euroskepticism."

Are there lessons to be learned for the SPD from Labour's transformation? Not really, according to Traugott. "If you look at the last 10 years, the Social Democrats in Germany and Labour in the UK went from a traditional working class party to the so-called Third Way represented by Blair and Schröder. Labour managed to stay together during this period and under Corbyn the party has moved back to the left. While in Germany, where this division happened with the SPD moving to the center and the economic liberal mainstream, the party split and spawned elements of Germany's Left Party."

Read more: Where will Europe's mega-election year 2017 leave the Left?

Another key element of Corbyn's appeal and success is that he has managed to tap into the support of young voters in the UK, in part through movements like Momentum, which as Lees points out has become "the intellectual force behind this sort of more creative end of the Corbyn revolution. But [you have to allow] such organizational models that are quite different to the SPD's instincts which are more command and control in the traditional social democratic mode."

A Social Democratic revolution?

According to Traugott, that's not something Schulz can copy one-to one. "You don't have the young revolutionist spirit in Germany like you do in the UK." 

Whether a revolution is the answer in particular to the SPD's woes is arguable. If by revolution the SPD and other Social Democratic parties mean a return to their traditional roots and beliefs, that could be the right approach.

"The Social Democratic parties are associated with a sort of failure to look after their own people and that's why the populist parties in particular have been able to step in and articulate the discontent that's out there. I think all of the Social Democratic parties in the period after the mid-90s under Blair, under Schröder lost sight of what they were there for," says Lees.